When converting the vector (-5.0, -7.0) into magnitude/angle form, what is the magnitude?

To find the magnitude of the vector (-5.0, -7.0), we use the formula for the magnitude of a vector, which is derived from the Pythagorean theorem. The magnitude is calculated as follows:

Magnitude = √(x² + y²)

Here, x = -5.0 and y = -7.0.

Plugging in the values:

Magnitude = √((-5.0)² + (-7.0)²)

= √(25 + 49)

= √74

≈ 8.6

This calculation leads to a magnitude result of approximately 8.6, confirming the correctness of this answer. Thus, when converting the vector into magnitude/angle form, the magnitude is accurately found to be approximately 8.6.